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GENUS FIELDS OF CYCLIC l-EXTENSIONS OF RATIONAL FUNCTION FIELDS

2013; World Scientific; Volume: 09; Issue: 05 Linguagem: Inglês

10.1142/s1793042113500243

1793-0421

Victor Bautista-Ancona, Martha Rzedowski–Calderón, Gabriel Villa–Salvador,

Advanced Mathematical Identities

We give a construction of genus fields for Kummer cyclic l-extensions of rational congruence function fields, l a prime number. First we find this genus field for a field contained in a cyclotomic function field using Leopoldt's construction by means of Dirichlet characters and the Hilbert class field defined by Rosen. The general case follows from this. This generalizes the result obtained by Peng for a cyclic extension of degree l.